Question

I NEED help pls! pic below

Answer 1

I will do what I can.

Answer 2

hint:
we can rewrite your equation as below:
\[\huge {2^{6x}} = {2^0}\]
since we have \(\Large 2^0=1\)

Answer 3

ok

Answer 4

I was say do it backwards, but.. nevermind. :P

Answer 5

now, we note that two powers, with the same base, are equals if also exponents are equals each other, so such equation above is \/equivalent\) to this one:
\[\huge 6x = 0\]

Answer 6

oops.. is \(equivalent\)...

Answer 7

now, please, divide both sides of the last equation by \(6\), what do you get?

Answer 8

1 and 0

Answer 9

hint:
we have:
\[\Large \frac{{6x}}{6} = \frac{0}{6}\]
and therefore: \(\Large x=0\), am I right?

Answer 10

ya sorry

Answer 11

correct! That is the solution for part A)

Answer 12

ok so what would i say for essay?

Answer 13

you have to write all my steps here

Answer 14

For part B, using the same reasoning of before (part A), we can rewrite the equation like below:
\[\huge {5^{0x}} = {5^0}\]
since, as before \(5^0=1\), then, we have to equate the exponents each to other, so such equation is equivalent to this one:

\( \huge 0x=0\)

Answer 15

now, please if I replace \(x=2\), we have:
left side= \(0 \cdot 2=...?\)
please continue

Answer 16

@horsegal244

Answer 17

sorry i was on the phone

Answer 18

@Michele_Laino

Answer 19

this is wha i said for part a

Answer 20

ok Now, for part B:
as I said before, if we replace \(x=2\) for example, we have:
left side = \(0 \cdot 2=...?\) please continue

Answer 21

0 x 2 = 0

Answer 22

better is "then we equate the exponents, so: \(6x=0\), subsequently, I divide both sides by \(6\) and I get \(6x/6=0/6\) from which I can write \(x=0\)"

Answer 23

is that after 2^6x?

Answer 24

yes!

Answer 25

ok part b

Answer 26

for part B, we get:
left side =\(0 \cdot 2=0\)
and right side =0, so we can conclude \(x=2\) is a solution of our exponential equation.
Now if I replace \(x=71\), then I get:
left side = \(0 \cdot 71=...?\)
please continue

Answer 27

= 0

Answer 28

correct! So, since right side =0, then I conclude that \(x=71\) is also a solution of the exponential equation
Now, as you can see I can replace any number, and I will reach the same conclusion, so how many solutions there are?

Answer 29

oops.. are there?

Answer 30

2?

Answer 31

If I replace \(x=218\) I get:
left side = \(0 \cdot 218=0\), so also \(x=218\) is a solution, as you can see I can replace \(any\) number, and such number is also a solution, so what can you conclude?

Answer 32

any number will come out with the same conclustion

Answer 33

so can you give me a hint on what i should say for part B on essay

Answer 34

ok! and how are these numbers?

Answer 35

i dont understand im sorry.

Answer 36

there are infinite numbers, right?

Answer 37

yes

Answer 38

then such exponential equation has infinite solutions

Answer 39

ok

Answer 40

so then what should i say?

Answer 41

so a possible answer is similar to the answer for part A, in particular, we can write this:
"...then we equate the exponents, so: \(0 \cdot x=0\), and such equation has infinite solutions, since every real number checks such equation. So, I conclude that the starting exponential equation has infinite solutions"

Answer 42

for part B? the whole problem

Answer 43

is that the whole problem?

Answer 44

yes! it is for part B), of course it is the last part, namely the complete answer can be this:

"If I apply the rule of power of power, I can rewrite that equation, like this: \(5^{0 \cdot x}= 5^0\). Then we equate the exponents, so: \(0⋅x=0\), and such equation has infinite solutions, since every real number checks such equation. So, I conclude that the starting exponential equation has infinite solutions"

Answer 45

can you help me with 3 more?

Answer 46

I'm very sorry, I can not :( since I have to help another student, he asked me for help 20 minutes ago!

Answer 47

and I have to help all of you!!